Brandubh 7x7

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Hagbard
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Re: Brandubh 7x7

Post by Hagbard » Sun Aug 14, 2016 10:00 pm

More Brandubh balances.

The Brandubh 7x7 game balance is at the moment measured to +1.34 (setup Brandubh cross 7x7).
To ensure that there aren't other setups with a finer balance, two alternative setups were tested: Brandubh cross no throne and Brandubh circle no throne, both without a throne.

Game balance results are:

Code: Select all

x . . b . . x
. b . . . b .
. . . w . . .
b . w k w . b
. . . w . . .
. b . . . b .
x . . b . . x
Brandubh circle no throne 7x7, balance -2.00 (15 games)

Code: Select all

x . . b . . x
. . . b . . .
. . . w . . .
b b w k w b b
. . . w . . .
. . . b . . .
x . . b . . x
Brandubh cross no throne 7x7, balance -2.75 (15 games)


So, best Brandubh setup is still the Brandubh cross 7x7, game balance +1.34
Last edited by Hagbard on Thu Mar 23, 2017 10:32 pm, edited 1 time in total.

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Hagbard
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Re: Brandubh 7x7

Post by Hagbard » Thu Jan 05, 2017 9:09 am

Summary on the Irish Brandubh:
http://aagenielsen.dk/brandubh_summary.php

mccluskeyp
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Re: Brandubh 7x7

Post by mccluskeyp » Tue Apr 17, 2018 8:28 pm

Question on corner captures in Brandubh. Below is an example.

1. There is an Attacker on square C1.
2. The King moves B2-B1.
3. A second Attacker moves B4-B2.

Does the second Attacker's move, B4-B2, capture the King in Brandubh? The King would be captured in Old Hnefatafl.

Thanks,
mccluskeyp

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Hagbard
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Re: Brandubh 7x7

Post by Hagbard » Wed Apr 18, 2018 9:59 am

mccluskeyp wrote:
Tue Apr 17, 2018 8:28 pm
Question on corner captures in Brandubh. Below is an example.

1. There is an Attacker on square C1.
2. The King moves B2-B1.
3. A second Attacker moves B4-B2.

Does the second Attacker's move, B4-B2, capture the King in Brandubh? The King would be captured in Old Hnefatafl.

Thanks,
mccluskeyp
In your example the king is safe and will in his next turn move to A1 and win.
In Brandubh the king is not captured by surrounding as is the case in Old Hnefatafl, and so the second Attacker's move B4-B2 has no effect.
In Brandubh the king is captured from 2 sides, and so the capturing attacker must move to C1 and capture the king against the corner.

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Hagbard
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Re: Brandubh 7x7

Post by Hagbard » Wed Apr 18, 2018 10:26 am

Hagbard wrote:
Wed Apr 18, 2018 9:59 am
In Brandubh the king is not captured by surrounding as is the case in Old Hnefatafl, and so the second Attacker's move B4-B2 has no effect.
In Brandubh the king is captured from 2 sides, and so the capturing attacker must move to C1 and capture the king against the corner.
Many years ago Adam, Tim and I had a discussion about how to interpret these two styles of capturing. We came to this way of seeing it:
Capturing from 4 sides models capturing the king alive, for demanding of ransom etc.
Capturing from 2 sides models killing the king, the same way soldiers are killed.

unhandyandy
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Re: Brandubh 7x7

Post by unhandyandy » Fri Dec 28, 2018 7:45 pm

cyningstan wrote:
Mon Aug 24, 2015 12:23 pm
Since last month I notice that the balance has changed, it's now at +1.22 overall (+1.31 when compensated for better players). That's not bad, but I've compared it to the game on Dragonheels' Lair that uses my old rules. Of 314 games, there were 144 white wins against 166 black, with 4 draws. Using Aage's notation that, I think, gives a balance of -1.15 overall. Thibaut doesn't separate out the better players' matches for extra stats.

I don't think that this is going to change my mind about changing my own site (and, eventually, books) to use Aage's rules. But I really have my fingers crossed that the balance doesn't creep further away from +1/-1 as more games are played on here.
So did you eventually change your mind? I've just looked at your Brandubh leaflet and the rules seem to be your original ones.

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Re: Brandubh 7x7

Post by Hagbard » Sat Jun 29, 2019 6:02 pm

Historical Hnefatafl 7x7 initial setup.
At the moment we use these setups for the Hist. Hnef. 7x7:

Brandubh (forbidden throne and corners):
Image
Ard Ri (no forbidden squares):
Image

Although the two setups are playable, the balances are not too good:
Brandubh balance +1.44
Ard Ri balance +1.47

The setups of game pieces for the two variants are the same, only some rule details differ, and it's interesting that the two balances end up practically the same.

Could setting the game pieces in another way result in better game balances?


An algorithm found all setups for the 7x7 board; there are 78 possible setups.
Ignoring setups where one party wins immediately or kills opponent pieces immediately, left are 9 setups.

Code: Select all

27.
- - - b - - -
- - - b - - -
- - - w - - -
b b w K w b b
- - - w - - -
- - - b - - -
- - - b - - -
Brandubh balance known +1.44

28 .
b - - b - - b
- - - - - - -
- - - w - - -
b - w K w - b
- - - w - - -
- - - - - - -
b - - b - - b

29.
- - - b - - -
- b - - - b -
- - - w - - -
b - w K w - b
- - - w - - -
- b - - - b -
- - - b - - -
Brandubh balance known +1.47

31 .
b - - - - - b
- - - b - - -
- - - w - - -
- b w K w b -
- - - w - - -
- - - b - - -
b - - - - - b

32.
- - - - - - -
- b - b - b -
- - - w - - -
- b w K w b -
- - - w - - -
- b - b - b -
- - - - - - -

34 .
b - - - - - b
- b - - - b -
- - - w - - -
- - w K w - -
- - - w - - -
- b - - - b -
b - - - - - b

37.
- b - - - b -
b - - - - - b
- - - w - - -
- - w K w - -
- - - w - - -
b - - - - - b
- b - - - b -
Not usable for Brandubh

38.
- - b - b - -
- - - - - - -
b - - w - - b
- - w K w - -
b - - w - - b
- - - - - - -
- - b - b - -
Brandubh balance known +1.82

39.
- - - - - - -
- - b - b - -
- b - w - b -
- - w K w - -
- b - w - b -
- - b - b - -
- - - - - - -

Hypothesis:
One or more of these setups could result in better 7x7 game balances.

And while we're at it: The Ard Ri should have a throne if possible, since the Buckquoy board clearly has a marked throne.
Last edited by Hagbard on Thu Jul 25, 2019 1:07 pm, edited 1 time in total.

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branan
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Re: Brandubh 7x7

Post by branan » Fri Jul 05, 2019 6:57 pm

Hi all.

Aage current test matches will show us if changing the starting position changes the balance of the game, i could be wrong, but I doubt it will change it enough.

I humbly think the rules should rather be slightly adapted to consider the small number of attackers compared to Tablut.

For example, the particular case of squares arround the throne could be modified to allow sandwiched captures of the King with only 2 attackers instead of 3, like this:

Rule 7a.png
King captured next the throne
Rule 7a.png (12.13 KiB) Viewed 858 times
This will only require 25% of all attackers to be done instead of the current 37.5%.

Another possibility could be to forbid the king from returning to his throne once he has left it.

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branan
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Re: Brandubh 7x7

Post by branan » Tue Sep 03, 2019 6:10 pm

branan wrote:
Fri Jul 05, 2019 6:57 pm
.../... the particular case of squares arround the throne could be modified to allow sandwiched captures of the King with only 2 attackers instead of 3, like this:

Rule 7a.png
Rule 7a.png (12.13 KiB) Viewed 858 times
This will only require 25% of all attackers to be done instead of the current 37.5%. .../...
Dear Brandubh players, may I have your opinion about this?

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Hagbard
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Re: Brandubh 7x7

Post by Hagbard » Wed Sep 04, 2019 12:38 pm

branan wrote:
Fri Jul 05, 2019 6:57 pm
I humbly think the rules should rather be slightly adapted to consider the small number of attackers compared to Tablut.

For example, the particular case of squares arround the throne could be modified to allow sandwiched captures of the King with only 2 attackers instead of 3, like this:


Rule 7a.png

This will only require 25% of all attackers to be done instead of the current 37.5%.

Another possibility could be to forbid the king from returning to his throne once he has left it.
Added to the games list for test:
"Brandubh king2nextthrone 7x7": King captured on squares next to the throne by 2 blacks instead of 3 blacks.
"Brandubh noreturn 7x7": King cannot return to throne.

Both would weaken white to some unknown degree.

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